I have not received your plots. But I can see the problem you have. Because the ion current is equal

I=g(V-Vr), where  I current, g channel conductance, V voltage, and Vr reversal potential. The channel conductance then is equal

g=I/(V-Vr).

When you calculate conductance the way you describe, you have a problem with the voltage that is close to your reversal point. This happens because at the voltage that is near the reversal point the difference between V and Vr is very small. When you divide your current on the very small value, you have your bump in the conductance.  It does not mean that your conductance in this point is very large. It just means that the way you calculate conductance gives you a very large error.

The correct way to calculate the dependence of a conductance as a function of voltage is as follows.

You need to plot an IV curve and then choose points on the curve where you want to calculate conductance.  For each of these points, you plot a tangent line and calculate a slope of this line. The value of the slope of a certain voltage is a conductance at this voltage.

This procedure is shown in the Figure (see attached file). The tangent line is drowning at the current corresponding to the voltage V1. The change of voltage in the arbitrary vicinity of V1 is  ΔV. It corresponds to the current change is ΔI. The conductance in the point V1 is equal ΔI/ΔV:

gv1= ΔI/ΔV

The repeating this procedure for as many voltage points as you wish (v1, V2,…) you will determine the dependence of conductance on voltage. The text and Figure are in the attached file.

This is great, Thank you.

But could you use the same formula for single channel conductance?

kind regards,

Refik

Dear Vitaly Vodyanoy

Thank you so much. It was really helpful. Now the issue is clear to me

So is there a way to calculate the slope of a IV curve in any statistical software? I use ORiginPro as my statistics software and I can not find a  way to calculate the slope of a non linear fit. 

I feel bad about my mathematical knowledge

Thank you again

Refic,

If your IV curve is for a single channel, then the slope will give you a conductance for this channel. You just need to watch units. You need to use Volts and Ampers to get conductance in Siemens.

Tharaka Darshana Wijerathne

You can find a techniques to determine a slope in Origin 8.6 in this link

https://www.youtube.com/watch?v=ApO-KTrxzQk

If you have a different version of Origin, you can use the idea of the method. I have seen that Origin 2016 has a special program for calculating slopes.

My best regards,

Vitaly

Thank you so much Vitaly Vodyanoy. 

Thank you Vitally. I appreciate it very much,Do I need to take into account the duration of the channel opening (flickering) or just use the amplitude at a given voltage? Also what happens at some voltages the channels open at two-or 3-folds?

There are a number of other approaches that could be used.

Firstly keep EK negative,  well below your holding potential, this will help with errors that arise when EK is close to your test potentials, so changing you intra and extracellular buffers may help.

alternatively you could plot tail currents on re-polarization against test voltage. I often hold at -80 to -40 mV and jump to the test potential to activate BK, then re-polarize to 0 mV and measure the tail currents.  A plot of tail currents against voltage should give you an idea  of the underlying conductance curve because all tail currents are measured at 0 mV and have the same underlying emf (0 mV-EK), also tail current amplitude is easy to convert to conductance. I  fit the tail currents to a single exponential to determine the tail current amplitudes.

hope this helps

I agree with Marcus, the simplest way to get a conductance voltage curve is to use a protocol as he suggests that evokes tail currents at a set voltage so the driving force is constant. You can then just plot normalized tail currents and you have a G-V curve without further calculations. You can fit this curve with a Boltzmann function in Origin (you can find it in non-linear curve fitting). This will give you the parameters for the voltage dependence of gating (V0.5 and slope).

Refik,

To study IV or gV characteristics you do not need to account the duration of the channel opening  or flickering but  just use the amplitude at a given voltage. If you study a channel kinetics (Open, closed time distributions, etc) you need to measure times. p-clamp software has a special program for analyses of  flickering. If you have your channels are piled up with the amplitude of 2 or 3 channels, then you are not dealing with a single channel fluctuation but with multiple channels. If you have a homogeneous channel system you may consider to use the full amplitude divided by a number of channels. However, if your system is composed from a different channels, you need to filter them and analyze one channel at the time. 

My best regards,

Vitaly

Thanks Vitaly,

That is great. Multiple channels, Yes they seem to be similar in amplitude and pile on top of each other. If the amplitude is identical, are they the same type or a different type? And also is it possible that same channel having multiple conducatnce states.

Tharaka, thanks for sharing your space.

many thanks, Refik

Refik

In the case you have multiple channels, the amplitude alone may not be a sufficient criterion for the identity of the channels. You need to analyze the kinetic properties, and the most importantly, to examine effects of specific blockers. Each state of the channel having multiple stated needs to be analyzed separately. For this case, you need to be able to control various state of conductance by blockers, or by genetic engineering, if you are dealing with the natural entity.

My best regards

Vitaly

Dear Warren. 

Thank you so much for the clear explanation.

I calculated the GV curve as you said from one of my reading from Slo3 (Voltage gated Potassium) ion channel (Image 1.1).  The point I used to obtain tail current is zoomed in the image 2 (Red arrow). I assume the blue arrow as capacitative current.

So I plotted the normalized tail current at blue arrow together with the calculated slope from normal IV Curve (image 3).  The two plots seems different. Can you please suggest any reasons. 

My step protocol is -100mV hold, +24mVx14 steps (300ms long). So the final step is +212mV. Gap between two steps is 4 seconds.

Solutions used are internal- 130KAsp 7.3pH and external 140Na+5K (I assume having asymmetrical Potassium concentrations is not going to be a problem. )

IV Curve calculated from STEP is at 4th image attached 

Thank you again

Hi,

I just finished a experiment to test the reversal potential. My protocol started from -55mv to +95mv with 30- mv increment , 6 sweeps in total. Now,I need plot the graph like your last figure, but I do not how to do it .So,could you show me more detailed steps on how to plot I-V relationship curve with Origin software?

Thanks a lot. 

Hi Huang Lumei

Im really sorry that I missed your question. I came back to read this thread after a long time. I can show you how to make the figures if it's not too late. Please let me know or contact me via [email protected]. Ill send you step by step instructions. 

:)

This response is quite late, but what works best for the BK channel is to make the G-V from the normalized tail current. If the tail potential is too negative, the deactivation kinetics is too fast (comparable to that of the capacitive current). To substract the capacitive current (and the leakage current), you need to make a subtraction P/N protocol.

Dear guys, I apologize for interfering.

There are two sorts of problems when measuring conductances. One is just technical resulting from experimental inaccuracy. But the suggestion to solve it by replacing g = I/V with g = dI/dV is a bit funny. There are two (at least) different definitions of conductance. One is the so-called chord conductance I/V, and the second one, the slope conductance dI/dV. These are two different entities, and they are not equal as soon as the V-I curve is not linear. This does not depend on experimenta noise and other factors.

As I said, chord and slope conductance are different measures, and the question of what is better, more accurate or more correct is meaningless. The real question is, what do you want to do further with your results. Then you choose what to calculate.

How to extract the two from noisy data is a separate question.

Dear Willy and Victor

Thank you so much or adding more insight in to the thread. I concluded my work related to the GV curves few months back with the help of the informative discussion here.

Evan though the original post is bit old, this thread gets a lot of reads regularly and I hope more people will get valuable information from this thread. Good to see the discussion is still progressing.

Again thank you all for the valuable responces

I endorse Victor's answer above as the most fundamental explanation. Mathematically it is simply the difference between taking the 1st order derivative of the I/V curve (G = dI/dV, or the equation of the continous gradient of the I/V curve) vs simply taking discrete conductance averages (G= I/V, linear average between any two defined Vm points or 'chord' conductance as Victor terms it).

But I agree entirely that it seems strange to be attempting to solve experimental inaccuracy with a mathematical analysis. The more important question is what is the source of the experimental error: is it real or is it really an experimental/instrumentational inaccuracy - answering this question has little to do with the post-collection analysis and manipulation of the data. In fact, to the contrary, you may disguise or miss some important data by taking the chord conductance between two random points simply in an attempt to 'smooth' the data. I approach this from a fundamental model fitting and data analysis point-of-view, so if I have missed something relevant that is specific to ion channel electrophysiology I apologise. With this caveat, I think Victor's answer is the most fundamentally useful.